1. How long does it take for each investment to be worth more than $7500?
2. What are the values of each investment after 3 years, 7 years, and 10 years?
Investment 1: 6.1% compounded quarterly
Investment 2: 6.1% compounded monthly
Calculating the Time for Each Investment to Reach $7500
To track the future values of the two investments, we can use a spreadsheet or a financial program on a calculator or computer. Let's start by calculating how long it takes for each investment to be worth more than $7500.
Investment 1: 6.1% compounded quarterly
Investment 2: 6.1% compounded monthly
To determine the time it takes for each investment to reach $7500, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
For Investment 1 (6.1% compounded quarterly), we have:
P = $5000
r = 6.1% = 0.061 (in decimal form)
n = 4 (compounded quarterly)
Let's solve for t:
$7500 = $5000(1 + 0.061/4)^(4t)
To find the time it takes for Investment 1 to be worth more than $7500, we need to solve this equation. However, since it involves an exponential term, we can use trial and error or a financial program to find the answer.
For Investment 2 (6.1% compounded monthly), we have:
P = $5000
r = 6.1% = 0.061 (in decimal form)
n = 12 (compounded monthly)
Similarly, let's solve for t:
$7500 = $5000(1 + 0.061/12)^(12t)
Again, we can use trial and error or a financial program to find the time it takes for Investment 2 to be worth more than $7500.